0x0009 - Project Euler 008

Problem:

Find the greatest product of five consecutive digits in the 1000-digit number.

73167176531330624919225119674426574742355349194934 96983520312774506326239578318016984801869478851843 85861560789112949495459501737958331952853208805511 12540698747158523863050715693290963295227443043557 66896648950445244523161731856403098711121722383113 62229893423380308135336276614282806444486645238749 30358907296290491560440772390713810515859307960866 70172427121883998797908792274921901699720888093776 65727333001053367881220235421809751254540594752243 52584907711670556013604839586446706324415722155397 53697817977846174064955149290862569321978468622482 83972241375657056057490261407972968652414535100474 82166370484403199890008895243450658541227588666881 16427171479924442928230863465674813919123162824586 17866458359124566529476545682848912883142607690042 24219022671055626321111109370544217506941658960408 07198403850962455444362981230987879927244284909188 84580156166097919133875499200524063689912560717606 05886116467109405077541002256983155200055935729725 71636269561882670428252483600823257530420752963450

Solution:

s = \
"73167176531330624919225119674426574742355349194934\
96983520312774506326239578318016984801869478851843\
85861560789112949495459501737958331952853208805511\
12540698747158523863050715693290963295227443043557\
66896648950445244523161731856403098711121722383113\
62229893423380308135336276614282806444486645238749\
30358907296290491560440772390713810515859307960866\
70172427121883998797908792274921901699720888093776\
65727333001053367881220235421809751254540594752243\
52584907711670556013604839586446706324415722155397\
53697817977846174064955149290862569321978468622482\
83972241375657056057490261407972968652414535100474\
82166370484403199890008895243450658541227588666881\
16427171479924442928230863465674813919123162824586\
17866458359124566529476545682848912883142607690042\
24219022671055626321111109370544217506941658960408\
07198403850962455444362981230987879927244284909188\
84580156166097919133875499200524063689912560717606\
05886116467109405077541002256983155200055935729725\
71636269561882670428252483600823257530420752963450"

max = 0
for i in range(0, len(s) - 4) :
    p = 1
    for j in range(i, i+5) :
        p *= int(s[j])
    if p > max:
        max = p

print max

Analysis:

The 1000-digit number is stored as a string in variable s. The backslash ‘\’ at the end of a line implies that the following physical line is actually in the same logical line of code.

The inner for loop is used to calculate the product of 5 consecutive digits: from index i to index i+4 where i is the looping variable of the outer for loop. The value of indices used by i are in the range 0 to 996, excluding 996. So, i varies as 0, 1, 2, 3, …, 994, 995. Also j varies from 0 to 996 + 4, i.e. 1000, excluding 1000. So j takes values from 0 to 999 (inclusive).

Initially, the variable max is assigned the value 0. In the inner loop, for every i, j varies from i to i+4 (inclusive). The product p (initialized to 1 for every i) is calculated for digits at s[j], which are s[i], s[i+1], s[i+2], s[i+3] and s[i+4]. If the current product, p is greater than the largest product until before p (max), then max is assigned the value of p. Finally, after 995 outer loops, the largest product max is printed to the standard output.

I tried to optimize the code by adding the case that whenever a zero is encountered, the product is not calculated and all future possibilities of considering that index for calculation of product are removed. However, the program took about 15 – 20% time longer to execute.

Running time:

Using Python 2.7 under Ubuntu 10.10 terminal, the program took 4.959 milliseconds to give the output.